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Expansion of (1-x-x^2)/(1-2x-x^2+x^4).
2

%I #7 Jun 14 2016 16:33:22

%S 1,1,2,5,11,26,61,143,336,789,1853,4352,10221,24005,56378,132409,

%T 310975,730354,1715305,4028555,9461440,22221081,52188297,122569120,

%U 287865097,676078233,1587833266,3729175645,8758319459,20569736330

%N Expansion of (1-x-x^2)/(1-2x-x^2+x^4).

%C Diagonal sums of generalized Pascal triangle A124216.

%H Harvey P. Dale, <a href="/A124217/b124217.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,0,-1).

%F a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, C(n-k,j)C(j,2(j-k))2^(j-k)}};

%t CoefficientList[Series[(1-x-x^2)/(1-2x-x^2+x^4),{x,0,40}],x] (* or *) LinearRecurrence[{2,1,0,-1},{1,1,2,5},40] (* _Harvey P. Dale_, Jun 14 2016 *)

%K easy,nonn

%O 0,3

%A _Paul Barry_, Oct 19 2006